Abstract
The orthogonality relation between arrows in the class of all morphisms of a given category C yields a "concrete" antitone Galois connection between the class of all subclasses of morphisms of C. For a class Sigma of morphisms of C, we denote by (perpendicular to)Sigma (resp., Sigma(perpendicular to)) the class of all morphisms f in C such that f perpendicular to g (resp., g perpendicular to f) for each morphism g in Sigma. A couple (Sigma, Gamma) of classes of morphisms is said to be an (orthogonal) prefactorization system if
Sigma(perpendicular to) = Gamma and (perpendicular to)Gamma = Sigma.
If, in addition the pfs satisfies
(perpendicular to)Sigma = Iso = Gamma(perpendicular to),
then it will be called a dense prefactorization system.
A pair (epsilon, M) of classes of morphisms in a category C is called an (orthogonal) factorization system if it is a prefactorization system and each morphism f in C has a factorization f = me, with e is an element of epsilon and m is an element of M. This paper provides several examples of factorization systems and dense factorization systems in the category Top of topological spaces.